2 Answers
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We didn't see the Narada arrive at Vulcan in the movie. We only saw it after the destruction of (minus the Enterprise) the Federation's fleet.

The Federation received a distress signal from Vulcan stating that they were experiencing seismic activity, and then all communication was cut off. As such we can't assume that there were no Vulcan defenses. It would be safe to assume that there were some, but that like nearly every other ship the Narada engaged, they were quickly destroyed.

The Narada's drill jammed communication, so it is likely that no one on the surface knew about it, as communication was out. The "elders" though were in the sacred area, where Spock found them, so it is likely that they were aware that something was wrong, just not what. Spock did not alert them that they were in danger, but rather just what sort of danger they were in.

When they experienced seismic activities, communications weren't out. That's why they were able to send distress signal.
– LoboFeb 28 '13 at 3:50

And, you don't need communication to see what's happening in the sky. There're things called telescopes and long-range sensors which could be used from the surface.
– LoboFeb 28 '13 at 3:53

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@SachinShekhar They sent the distress signal, but obviously didn't know what was happening (as they called it seismic activities). If any individuals manning the telescopes and/or long-range sensors did find out (which again is likely as you point out) they had no way of organizing a defense force, as they were being jammed at that time. (Not only could they not communicate remotely, they couldn't even transport to deliver the message in person). As I stated in my answer, they were aware that they were in some sort of danger, just not exactly what.
– NominSimFeb 28 '13 at 14:17

On the battle cruiser issue, I’m not sure we’ve ever seen Vulcan military ships in Star Trek. As a race, they seem to be almost exclusively scientists and diplomats, and never seem to get involved in wars like the major Alpha Quadrant powers do.

It does seem odd that a prominent race like theirs is so theoretically vulnerable to being conquered by force. Maybe it turns out that logic and a nerve pinch are just as effective as phasers and photon torpedos.